A push is an aggressive act regardless of context, regardless of motives.
Be careful not to jump definitions. Aggressive, in the way you use it, is not derived from Aggression as libertarians use the term for the NAP. I might aggressively (making an all-out effort to win or succeed) save someone’s life without committing aggression, in the libertarian sense of the word.
The motives is why the pushee will forgive the pusher.
Let us concern ourselves with a case where the pushee does not forgive. Would you sersiously support his claim of damages? That would be silly.
If we begin taking motives into account rather than objective actions, we quickly run into contradictions, like saying it’s okay to use aggression to tax someone because it’s for the benefit of society :\
That’s not a contradiction, it’s simply wrong. We have to take ends, motives as you say, into account, because it is an inherent part of human action. We cannot say what an act is without the human intent. Without the intent, it is not fully an act.
When I push someone out of the way of a bus, my action is to save their life. If my action has been one of saving a life, this is not aggression, pure and simple.
If you push someone to save them and end up injuring them too, they could in theory still sue. Lots of would-be rescuers have also made the situation worse by trying and have been legitimately sued also. Like the girl with a broken neck whose rescuerspicked her up and by that made her into a quadraplegic.
But this doesn’t advance your argument. If I am negligent and do more harm than good in my attempt to save someone, then I must pay restitution, of course. This has nothing to do with whether or not a shove must always be an act of aggression.